Cognitive fullduplex relay networks under the peak interference power constraint of multiple primary users
 XuanToan Doan^{1},
 NamPhong Nguyen^{1},
 Cheng Yin^{1},
 Daniel B. da Costa^{2} and
 Trung Q. Duong^{1}Email authorView ORCID ID profile
https://doi.org/10.1186/s136380160794y
© Doan et al. 2017
Received: 12 June 2016
Accepted: 12 December 2016
Published: 5 January 2017
Abstract
This paper investigates the outage performance of cognitive spectrumsharing multirelay networks in which the relays operate in a fullduplex (FD) mode and employ the decodeandforward (DF) protocol. Two relay selection schemes, i.e., partial relay selection (PRS) and optimal relay selection (ORS), are considered to enhance the system performance. New exact expressions for the outage probability (OP) in both schemes are derived based on which an asymptotic analysis is carried out. The results show that the ORS strategy outperforms PRS in terms of OP, and increasing the number of FD relays can significantly improve the system performance. Moreover, novel analytical results provide additional insights for system design. In particular, from the viewpoint of FD concept, the primary network parameters (i.e., peak interference at the primary receivers, number of primary receivers, and their locations) should be carefully considered since they significantly affect the secondary network performance.
Keywords
1 Introduction
The explosion of data traffic over wireless communication has brought a huge demand for spectrum resources. Cognitive radio has arisen as a promising technology for efficiently utilizing the limited spectrum [1, 2]. The key principle behind the functionality of a spectrum sharing approach (also known as underlay strategy) in cognitive radio networks (CRNs) is that unlicensed secondary users are allowed to access the licensed spectrum as long as the interference from the secondary transmitters is harmless to the primary receivers [3]. In order words, the secondary transmitters need to set their transmit powers in order to not cause any interference to the primary network that is above a predefined level. This power adjustment implies a reduction in the coverage area of the secondary network. Fortunately, cooperative relay schemes, which can enhance the coverage of wireless networks by deploying helping nodes to transfer information from the source to the destination, have been introduced in CRNs with spectrumsharing environment (see, for instance, [4–8]). Specifically, different relay selection schemes assuming amplifyandforward (AF) and decodeandforward (DF) relaying protocols, were studied in [6–8], and the results showed that by applying appropriate cooperative schemes, cognitive relay networks can significantly attain improved performance.

Two relay selection schemes, namely, optimal relay selection (ORS) and partial relay selection (PRS), based on the availability of the system CSI at the secondary information source are proposed.

Due to the existence of the common random variables (RVs), i.e., the channels from the source and/or selected relay to multiple primary receivers, the signaltonoiseratios (SNRs) of all links become correlated which makes the analysis troublesome. To get around this challenge, we first apply the conditional probability on these RVs and then derive the analytical expressions for the OP of the considered system. Specifically, the exact and asymptotic expressions of OP in PRS and ORS schemes are also obtained.

The derived results reveal several insights. For instance, it is shown that the primary network’s parameters, i.e., the peak interference constraint, the distance from the primary receivers to the secondary transmitters, and the number of primary receivers, have a high impact on the performance of the secondary network and should be carefully designed. In addition, ORS strategy outperforms PRS 1 in terms of OP, and increasing the number of FD relays can significantly improve the system performance.
The rest of this paper is organized as follows. The system and channel models are introduced in Section 2. Exact and asymptotic expressions for the OP assuming ORS and PRS policies are derived in Sections 3 and 4, respectively. Numerical results are presented in Section 5, which are corroborated through Monte Carlo simulations. Finally, the main conclusions are outlined in Section 6. Appendices A, B, C, and D present the proofs of four Lemmas.
2 System and channel models
where \(\mathcal {P}_{\mathsf {S}}\) and \(\mathcal {P}_{\mathsf {R}}\) are the transmit powers of S and R _{ k }, respectively, \(h_{\mathsf {S} \mathsf {P}_{m}}\phantom {\dot {i}\!}\) and \(\phantom {\dot {i}\!}h_{\mathsf {R}_{k} \mathsf {P}_{m}}\) denote the channel coefficients pertaining to the S→P _{ m } and R _{ k }→P _{ m } links, respectively. The CSI of the channel gains from the source and relays to primary users can be obtained from direct feedback from PURx or indirect feedback from band manager [22].
where x _{ S } and x _{ R } represent the transmitted signals from S and \(\mathsf {R}_{k^{*}}\phantom {\dot {i}\!}\), respectively, \(h_{\mathsf {S} \mathsf {R}_{k^{*}}}\phantom {\dot {i}\!}\) is the channel coefficient from S to \(\phantom {\dot {i}\!}\mathsf {R}_{k^{*}}\), and \(\phantom {\dot {i}\!}n_{\mathsf {R}} \sim \mathcal {N}(0,N_{0})\) is the additive white Gaussian noise (AWGN) at \(\mathsf {R}_{k^{*}}\phantom {\dot {i}\!}\).
where \(h_{\mathsf {R}_{k^{*}} \mathsf {D}}\phantom {\dot {i}\!}\) denotes the channel coefficient from \(\phantom {\dot {i}\!}\mathsf {R}_{k^{*}}\) to D and \(\phantom {\dot {i}\!}n_{\mathsf {D}} \sim \mathcal {N}(0,N_{0})\) stands for the AWGN term at D.
Knowing that the OP is defined as the probability that the channel capacity of the considered system falls below a given threshold, such a metric can be formulated as
where denotes probability, \(F_{\gamma _{k^{*}}}(\cdot)\phantom {\dot {i}\!}\) represents the cumulative distribution function (CDF) of \(\phantom {\dot {i}\!}\gamma _{k^{*}}\), \(\phantom {\dot {i}\!}\beta = 2^{R_{\text {th}}}1\), and R _{th} is the target rate of the secondary network.
3 Outage probability analysis
3.1 Partial relay selection (PRS)
From (11)–(13), we have the following lemma.
where _{2} F _{1}(·,·;·;·) symbolizes the Gaussian hypergeometric function ([27], Eq. (9.14.1)) and \(\lambda _{X}^{1}\) is the mean value of exponential random variable h _{ X }^{2}, X∈{SR _{ k },R _{ k } D,SP _{ m },R _{ k } P _{ m },R _{ k }}.
Proof
The proof is given in Appendix A. □
3.2 Optimal relay selection (ORS)
From (15)–(17), we have the following lemma.
Lemma 2
The OP of the considered ORS scheme is given as follows:
Proof
The proof is given in Appendix B. □
4 Asymptotic outage analysis
In this section, an asymptotic outage analysis is carried out in order to gain further insights into the system performance. As will be shown, the considered system has null diversity order because of the selfinterference effect inherent to the FD technique^{2}. In addition, from the asymptotic expressions, we can observe that in the high SNR regime, the performance of the considered system does not depend on the channel of the second hop. In other words, to enhance the performance of the considered system, the performance of the first hop must be strengthen.
4.1 Partial relay selection
Proof
The proof is given in Appendix C. □
4.2 Optimal relay selection
Lemma 4
In the high SNR regime, the OP of the considered system with ORS scheme can be expressed as
Proof
The proof is given in Appendix D. □
5 Numerical results and discussions
In this section, numerical examples are presented to show the impact of the network’s parameters on the overall system performance. The accuracy of our analysis is attested by Monte Carlo simulations, in which a perfect agreement between the analytical and simulated curves is observed. Without loss of generality, we adopt a twodimensional topology in which the coordinates (x,y) of S, R, and D are (0,0), (2,0), and (3,0), respectively. Thus, the Euclidian distance between the nodes can be calculated as \(d_{AB} = \sqrt {(x_{A}x_{B})^{2} + (y_{A}y_{B})^{2}}\), where A is placed at (x _{ A },y _{ A }) and B has the coordinate (x _{ B },y _{ B }). In order to take the pathloss into account, we assume \(\lambda _{X} = d_{X}^{\alpha }\), where α denotes the pathloss exponent and λ _{ X }∈{λ _{ SP },λ _{ SR },λ _{ RP },λ _{ RD },}. Without loss of generality, in the plots, we set α=4 and the target rate of the secondary network R _{th}=0.4 bits/s/Hz, and λ _{ R }=22.
6 Conclusions
In this paper, the system performance in terms of outage probability of a cognitive FD relay network in the presence of multiple primary receivers has been evaluated. In particular, two relay selection strategies, namely ORS and PRS, have been proposed to enhance the performance of the system. New exact and asymptotic expressions for the OP of the PRS and ORS schemes were derived. The results showed that the ORS scheme has a better performance than PRS scheme. In addition, increasing the number of FD relays can enhance the system performance. Primary network designing parameters, i.e., the peak interference constraint, the number of primary receivers, and their locations, have great influences on the performance of the secondary network and should be mindfully considered.
7 Endnotes
^{1} Dualantenna FD implementation is one of many ways to deploy FD mode, including singleantenna FD implementation.
^{2} In the considered system, the transmit power at the fullduplex relay is nonoptimal. A transmit power optimization scheme at fullduplex relay can be considered to restrain the selfinterference effect.
8 Appendix A: Proof of Lemma 1
In order to derive \(F_{\gamma _{k^{\ast }}^{\mathsf {PRS}}}(\beta)\), we need to determine \({F_{\gamma _{1k^{\ast }}^{\mathsf {PRS}}\mathcal {X}_{4}}}{\beta }\) and \(F_{\gamma _{2k^{\ast }}^{\mathsf {PRS}}\mathcal {X}_{4}}(\beta)\). In this case, \(F_{\gamma _{1k^{\ast }}^{\mathsf {PRS}}\mathcal {X}_{4}}(\beta)\) can be written as
Similarly, \(F_{\gamma _{1k^{\ast }}^{\mathsf {PRS}}\mathcal {X}_{4}}(\beta)\) can be calculated as
where Ei(·) denotes the exponential integral function and (??) is obtained with the help of ([27], Eq. (3.351)). By substituting (??) and (??) into (33), (??) is attained.
9 Appendix B: Proof of Lemma 2
On the other hand, the CDF of γ _{2k } conditioned on \(\mathcal {Y}_{4k}\) can be calculated as
Finally, the CDF of γ _{1k } conditioned on \(\mathcal {X}_{2}\) and \(\mathcal {Y}_{4k}\) can be calculated as
where \(F_{{\mathcal {Y}_{1k}}}\left ({x}\right) = 1 \exp \left (\lambda _{\mathsf {S}\mathsf {R}} x\right) \) and \(f_{{\mathcal {Y}_{3k}}}\left ({x}\right) = \lambda _{\mathsf {R}} \exp \left (\lambda _{\mathsf {R}} x\right) \).
into (38), (??) is attained.
10 Appendix C: Proof of Lemma 3
where step (a) is obtained by using the McLaurin expansion of exp(x) and neglecting the high order items for small x.
where step (b) is performed by neglecting the high order terms. By substituting (42) into (44), and after some mathematical manipulations, (??) is obtained.
11 Appendix D: Proof of Lemma 4
where steps (c) and (d) are performed by using the McLaurin expansion of exp(x) and neglecting the high order terms for small x.
into (38), (??) is obtained.
Declarations
Acknowledgements
This work was supported by the Newton Institutional Link under Grant ID 172719890.
Competing interests
The authors declare that they have no competing interests.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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